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The horoboundary and isometry group of Thurston's Lipschitz metric

Cormac Walsh 1, 2 
1 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We show that the horofunction boundary of Teichmüller space with Thurston's Lipschitz metric is the same as the Thurston boundary. We use this to determine the isometry group of the Lipschitz metric, apart from in some exceptional cases. We also show that the Teichmüller spaces of different surfaces, when endowed with this metric, are not isometric, again with some possible exceptions of low genus.
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Submitted on : Monday, December 29, 2014 - 7:35:19 PM
Last modification on : Saturday, June 25, 2022 - 7:44:00 PM

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  • HAL Id : hal-01098838, version 1
  • ARXIV : 1006.2158



Cormac Walsh. The horoboundary and isometry group of Thurston's Lipschitz metric. Athanase Papadopoulos. Handbook of Teichmüller Theory, Volume IV, 19, European Mathematical Society, pp.838, 2014, IRMA Lectures in Mathematics and Theoretical Physics, 978-3-03719-117-0. ⟨hal-01098838⟩



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